There is a road of equal width around the outside of a rectangular play ground having the length 45 m and breadth 40 m and the area of the roda is 450 sq-m.

Explanation

Let the breadth of the road =x m.
`:.` the length of the field including road `=(45+x+x)m=(2x+45)m`.
and the breadth of the field including road `=(40+x+x)m=(2x+40)m`.
`:.` Area of field including road `=(2x+45)(2x+40)sq-m`.
and area of field excluding road `=45xx40sq-m=1800sq-m`.
`:.` area of the road `={(2x+45)(2x+40)-1800=450`.
As per question, `(2x+45)(2x+40)-1800=450`.
or, `4x^(2)+90x+80x+1800=450`,
or, `4x^(2)+170x-450=0`
or, `2x^(2)+85x-225=0`
Hence the required quadratic equation is `2x^(2)+85x-225=0`.